Evaluate the integral. (Use C for the constant of integration. Enter your answer using function notation - use ln(x) instead of ln x.)

Step-by-step explanation:

Given

Required

Integrate

Using partial fraction, we have:

Take LCM

Cancel out the denominators

Open brackets

Collect like terms

Compare like terms on opposite sides

Subtract from

Subtract from

So, we have:

The integral becomes:

Split:

Split

Integrate

Hence:

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)

-3.5 is the distance.

i've had this question so choose the one in the absolute value sign.